25) While teaching the concept of squares and square roots, a teacher writes a series of odd numbers beginning from 1. S/He tries to show a pattern in the following way: 1 = 1 1+3=4=2² 1+3+5=9=3² 1+3+5+7=16=42 and so on. S/He does so to : Entertain learners (1) (2) Show an arithmetic progression (3) Help learners deduce a general mathematical fact (4) Puzzle the learners
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Step-by-step explanation:
The teacher is aiming to help learners deduce a general mathematical fact. By presenting a series of odd numbers and demonstrating the relationship between the sum of consecutive odd numbers and perfect squares, the teacher is illustrating the concept that the sum of the first \( n \) odd numbers is equal to \( n^2 \). This is a mathematical pattern known as the sum of consecutive odd numbers. The teacher's intention is to guide students towards recognizing and understanding this mathematical principle through a visual and interactive approach.